Abstract
Recently, Sasaki et al. presented an approximate factorization algorithm of multivariate polynomials. The algorithm calculates irreducible factors by investigating linear combinations of the same power of approximate roots. In this paper, we show that various kinds of multivariate polynomial factorizations can be performed by this method. We present algorithms for factorization of multivariate polynomials over power-series rings, over the integers, over algebraic number fields including algebraically closed fields, and over algebraic function fields. Furthermore, we discuss applicability of this method to univariate polynomial factorization.
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